Problem: Simplify the following expression: $ t = \dfrac{6q + 8}{8q} + \dfrac{8}{5} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{6q + 8}{8q} \times \dfrac{5}{5} = \dfrac{30q + 40}{40q} $ Multiply the second expression by $\dfrac{8q}{8q}$ $ \dfrac{8}{5} \times \dfrac{8q}{8q} = \dfrac{64q}{40q} $ Therefore $ t = \dfrac{30q + 40}{40q} + \dfrac{64q}{40q} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{30q + 40 + 64q}{40q} $ $t = \dfrac{94q + 40}{40q}$ Simplify the expression by dividing the numerator and denominator by 2: $t = \dfrac{47q + 20}{20q}$